ACT Essential Skills and Modeling Practice Test

Rates, unit conversions, ratios, percents and real-world graphs. Here are 10 ACT essential skills and modeling questions, each with the answer and the reason.

Updated 2026-11-14 by the Tigertest team. Original passages and questions written to the enhanced ACT format (2025): four choices, 50/45/36/40 questions, Science optional. Not affiliated with ACT, Inc. Score estimates are unofficial.

1.
What is $35\%$ of $80$ ?
- A.
  $2.8$
- B.
  $28$
- C.
  $45$
- D.
  $115$
Answer: B.
Write the percent as a decimal and multiply: $0.35 \times 80 = 28$ . You can also reason that $10\%$ of $80$ is $8$ , so $30\%$ is $24$ and $5\%$ is $4$ , giving $24 + 4 = 28$ . The choice $45$ comes from subtracting $35$ from $80$ , which is not what percent of a number means, and $2.8$ places the decimal point in the wrong spot.
2.
In a class, the ratio of boys to girls is $3:5$ . If there are $40$ students in the class, how many of them are girls?
- A.
  $15$
- B.
  $24$
- C.
  $25$
- D.
  $30$
Answer: C.
A ratio of $3:5$ means that out of every $3 + 5 = 8$ students, $5$ are girls. Since $40 \div 8 = 5$ , there are $5$ groups of $8$ , so $5 \times 5 = 25$ girls. The choice $15$ is the number of boys ( $3 \times 5$ ), and $24$ comes from treating $\frac{3}{5}$ of $40$ as the number of girls.
3.
A pump moves water at a constant rate of $4.5$ liters per second. How many hours will it take the pump to fill an empty tank that holds $81{,}000$ liters?
- A.
  $0.5$
- B.
  $3$
- C.
  $5$
- D.
  $300$
Answer: C.
Time is volume divided by rate: $81{,}000 \div 4.5 = 18{,}000$ seconds. There are $60 \times 60 = 3600$ seconds in an hour, so $18{,}000 \div 3600 = 5$ hours. The choice $300$ is the time in minutes ( $18{,}000 \div 60$ ), which is the answer if you stop after only one unit conversion. The choice $3$ comes from dividing by $6000$ instead of $3600$ .
4.
A ride-share service charges a $3.50 pickup fee plus $1.75 per mile. Dana can spend at most $30.00 on a ride. What is the greatest whole number of miles Dana can ride?
- A.
  14
- B.
  15
- C.
  16
- D.
  17
Answer: B.
Let $m$ be the number of miles. The cost must satisfy $3.50 + 1.75m \le 30$ , so $1.75m \le 26.50$ and $m \le 15.14$ . The greatest whole number of miles is 15, which costs $3.50 + 26.25 = \$29.75$ . Choice C rounds 15.14 up, which would cost $31.50 and exceed the budget, and choice D ignores the pickup fee entirely.
5.
In a first-period class of 20 students, the mean score on a test was 80. In a second-period class of 30 students, the mean score on the same test was 90. What is the mean score for all 50 students?
- A.
  84
- B.
  85
- C.
  86
- D.
  88
Answer: C.
A combined mean is the total of all the scores divided by the total number of students, not the average of the two means. The first class scored $20 \times 80 = 1{,}600$ points in all and the second $30 \times 90 = 2{,}700$ , so the combined mean is $\dfrac{4{,}300}{50} = 86$ . Choice B averages 80 and 90 as if the classes were the same size; the larger class pulls the mean closer to 90.
6.
A locker code consists of 4 different digits chosen from 1, 2, 3, 4, 5, 6, and 7, and the first digit must be odd. How many different codes are possible?
- A.
  480
- B.
  840
- C.
  1,680
- D.
  2,401
Answer: A.
Fill the restricted position first. There are 4 odd digits (1, 3, 5, 7) for the first position. Because digits cannot repeat, 6 digits remain for the second position, 5 for the third, and 4 for the fourth, so the total is $4 \times 6 \times 5 \times 4 = 480$ . Choice B, $7 \times 6 \times 5 \times 4 = 840$ , is the count without the odd-first restriction. Choice D, $7^4$ , allows digits to repeat and ignores the restriction.
7.
A bread recipe uses flour and sugar in the ratio $5:2$ . If a baker uses 15 cups of flour, how many cups of sugar should the baker use?
- A.
  $3.75$
- B.
  $6$
- C.
  $7.5$
- D.
  $37.5$
Answer: B.
Set up the proportion $\frac{5}{2} = \frac{15}{s}$ . Since $15$ is $3$ times $5$ , the sugar is $3$ times $2$ , so $s = 6$ cups. The choice $37.5$ comes from multiplying $15 \times 5 \div 2$ instead of $15 \times 2 \div 5$ , and $7.5$ is half of the flour rather than two fifths of it.
8.
Marcus has an average (arithmetic mean) score of 82 on his first 4 chemistry tests. What score does he need on his 5th test so that his average over all 5 tests is exactly 85?
- A.
  $85$
- B.
  $88$
- C.
  $94$
- D.
  $97$
Answer: D.
An average of $85$ over $5$ tests requires a total of $5 \times 85 = 425$ points. The first 4 tests total $4 \times 82 = 328$ points, so the 5th test must be $425 - 328 = 97$ . The choice $88$ comes from adding the $3$ -point gap to the old average once, but the 5th score has to make up that gap for each of the 4 earlier tests as well.
9.
A bacteria culture starts with 500 cells, and the population doubles every 3 hours. If the population keeps doubling at this rate, how many cells will be in the culture after 12 hours?
- A.
  2,000
- B.
  4,000
- C.
  8,000
- D.
  16,000
Answer: C.
In 12 hours there are $12 \div 3 = 4$ doubling periods, so the population is multiplied by $2^4 = 16$ : $500 \times 16 = 8{,}000$ cells. Choice A multiplies 500 by 4 instead of by $2^4$ , treating four doublings as a single factor of 4. Choice D uses five doublings, which would take 15 hours.
10.
An inlet pipe can fill an empty tank in 6 hours. A drain at the bottom of the tank can empty the full tank in 9 hours. If the tank starts empty and both the inlet pipe and the drain are open, how many hours will it take to fill the tank?
- A.
  3.6
- B.
  7.5
- C.
  15
- D.
  18
Answer: D.
The inlet fills $\dfrac{1}{6}$ of the tank per hour while the drain removes $\dfrac{1}{9}$ per hour, so the net rate is $\dfrac{1}{6} - \dfrac{1}{9} = \dfrac{3}{18} - \dfrac{2}{18} = \dfrac{1}{18}$ of the tank per hour. Filling the whole tank at that rate takes 18 hours. Choice A adds the rates, as if the drain were a second inlet pipe, and choice C simply adds the two times.

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